Related papers: Complete Characterization of Mixing Time for the C…
We study discrete quantum dynamics where single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often non-Markovian memory effects are attributed to structured environments…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW, and (ii)…
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
The coherent superposition of position states in a quantum walk (QW) can be precisely engineered towards the desired distributions to meet the need of quantum information applications. The coherent distribution can make full use of quantum…
Non-Markovian quantum effects are typically observed in systems interacting with structured reservoirs. Discrete-time quantum walks are prime example of such systems in which, quantum memory arises due to the controlled interaction between…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time…
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider…
We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum…
This paper studies the random walk on the hypercube $(\mathbb{Z}/2\mathbb{Z})^n$ which at each step flips $k$ randomly chosen coordinates. We prove that the mixing time for this walk is of order $\frac{n}{k} \log n$. We also prove that if…
Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we…
Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more…
We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…
In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter $\theta$ by performing…
We consider one-dimensional excited random walks (ERWs) with i.i.d. markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple…
Decoherence induced by coupling a system with an environment may display universal features. Here we demostrate that when the coupling to the system drives a quantum phase transition in the environment, the temporal decay of quantum…
We show by general arguments that networks whose density of states contains few highly degenerate eigenvalues result in inefficient performances of continuous-time quantum walks (CTQW) over these networks, while systems whose eigenvalues…
We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior…
We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the…